Abstract
This paper investigates two important analytical properties of hyperbolic-polynomial penalized splines, HP-splines for short. HP-splines, obtained by combining a special type of difference penalty with hyperbolic-polynomial B-splines (HB-splines), were recently introduced by the authors as a generalization of P-splines. HB-splines are bell-shaped basis functions consisting of segments made of real exponentials eαx,e−αx and linear functions multiplied by these exponentials, xe+αx and xe−αx. Here, we show that these types of penalized splines reproduce functions in the space {e−αx,xe−αx}, that is they fit exponential data exactly. Moreover, we show that they conserve the first and second ‘exponential’ moments.
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